Wilks’ theorem for semiparametric regressions with weakly dependent data
Marie du Roy de Chaumaray, Matthieu Marbac, Valentin Patilea
The Annals of Statistics · 2021 · Volume 49 · Issue 6
Abstract
The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the present and past values of a vector of covariates. A parametric model for the conditional variance of the series is added to capture further nonlinear effects. We propose suitable moment equations which characterize the mean and variance model. We derive an empirical log-likelihood ratio which includes nonparametric estimators of several functions, and we show that this ratio behaves asymptotically as if the functions were given.
Keywords
62F03, 62G20, 62M10, kernel smoothing, nonlinear time series, nuisance function, Parametric inference, pivotal statistic, α-mixing
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